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\title{A Sample of HPCC Opportunities in Fianancial Modeling\\
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\author{Miloje S. Makivi\'c\footnote{
Northeast Parallel Architectures Center (NPAC), Syracuse University,\\
111 College Place, Syracuse, NY 13244-4100\\ 
{\bf e-mail}: miloje@npac.syr.edu\\ 
{\bf Mosaic} http://www.npac.syr.edu/users/miloje/\\}
}
\date{\today}
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%\centerline{NPAC Technical Report SCCS ###}
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\centerline{\bf Abstract}
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\begin{abstract}
This report contains a brief exposition of HPCC enabled 
products and applications 
that can be developed by joint effort at NPAC and MHPCC. 
%\footnote{Copyright \copyright 1994 by Miloje S. Makivi\'c}\\
{\bf Keywords:} Derivative valuation, asset allocation, hedging,
parallel computing, data mining, World Wide Web, Simulation on
Demand, futures, options,
object-oriented technology.

\end{abstract}
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\widetext
\section{Introduction}
\label{sec:intro}
The role of high-performance computing and particularly parallel
computing in investment and commercial banking is likely to grow in
importance due to a convergence of the following factors:
\begin{itemize}
\item Increased volatility due to globalization of financial markets
\item Increase in complexity of derivatives and other risk management vehicles
\item Increased demand for real-time investment and asset allocation decision support
\item Increased volume of raw data and need to process large databases
\item Increased volume on the retail side of the spectrum mainly due to on-line technologies (Internet and WWW)
\item Resources for investment decision support
\end{itemize}
Two of the most promising application areas for parallel and distributed computing are:
\begin{itemize}
\item Support for Quantitative Analysis:
\begin{enumerate}
\item Derivative pricing
\item Portfolio optimization, valuation and asset allocation
\item Hedging (in real time)
\item Computational support for arbitrage trading
\item Risk Management simulations
\end{enumerate}
\item Data Mining
\begin{enumerate}
\item Detection of trends
\item Detection of fraud
\item Market segmentation
\item Development of hedging or arbitrage strategies based on historical patterns and analogies
\end{enumerate}
\end{itemize}
NPAC and MHPCC are well positioned to develop products and services in either of these categories,
although we have more experience and software for Quantitative Analysis applications.
It should be stressed that the listed applications constitute only a tip of the iceberg
of the opportunities for parallel and distributed computing in financial modeling. 
We may be able to prototype new products and services resulting from interactions with potential
clients, even though they will hinge on some of the core Quantitative Analysis or Data Mining applications.
One venue worth exploring is a combination of Quantitative Analysis or Data Mining software with advanced
visualization methods, such as Virtual Reality interface. This may provide a good synergy between
existing efforts at NPAC and MHPCC.


\section{Technical Aspect}
\label{sec:app}

Derivative pricing is one of the most compute intensive tasks in financial engineering.
Under crude approximations it is possible to obtain derivative prices quickly
using analytical methods, but they are not suitable for many real world situations.
There are three methods which are used in this context:
\begin{enumerate}
\item Numerical solution of the generalized Black-Scholes partial differential equation
\item Methods based on binomial and multinomial trees
\item Risk neutral valuation which hinges on Monte Carlo simulations
\end{enumerate}
Of these, Monte Carlo is the simplest to parallelize, and it also offers many other
advantages such as flexibility and possibility to price path-dependant options.
It is generally considered slow in the financial engineering community and therefore it
is considered more of a research tool for complex and/or exotic options. This view however
is far from true in a massively parallel environment since Monte Carlo offers practically
unlimited scalability unlike the other two methods. We have developed a novel version of
the Monte Carlo method which is capable of extracting complete information about an option
price, including its parameter sensitivities, in a single simulation. There is no other
method at present with the same capability. This capability is very important in practical
applications since option price sensitivities (known as greeks in the trader jargon) are
crucial for hedging and speculation. We have Monte Carlo option pricing
software with basic functionality running in parallel on SP-2.
An experimental version of this method is developed in Fortran 90 and being ported to HPF.

Methods based on binomial and multinomial trees have the advantage that they can quickly
price American contracts, which is not as straightforward using Monte Carlo. We have developed
binomial option pricing software on a variety of parallel platforms, and used this software to
demonstrate system integration capabilities of data flow environments such as AVS.

We also have a student working on parallelization of the Black-Scholes partial differential
equation. In addition to conventional domain decomposition techniques, she is developing a new
parallel method to compute the solution of the Black-Scholes equation for one parameter set
using a previously computed solution for a nearby parameter set. This method eliminates the
need for sequential time-stepping. This method hinges on the fact that a trader needs to
quickly value an option for a range of parameters. The method is not implemented yet on any parallel machine.

Risk management is one of the buzzwords in finance and banking these days, which is partially due
to the fear from derivatives inspired by Barings and Orange County fiasco. In addition, financial
institutions are forced to operate in a global environment which increases short time scale volatility.
Given that complexity of off-balance-sheet instruments used to hedge an institutions assets have
grown immensely, it is not surprising that sophisticated risk management capabilities with almost
real time capability must be established in many institutions. For bigger players, the demands on these
systems will soon grow to the point where they can be met by parallel compute servers only.
One of the methods of choice in risk management applications is Monte Carlo simulation. We have
developed a sequential Monte Carlo simulation engine for a prominent Wall Street software vendor
(Sailfish, Inc.) which specializes in high-end, all-encompassing risk management systems. We also have developed
a number of other modules which support risk management functions such as parameter estimation
for stochastic processes and large scale global optimization methods. 

Parameter estimation and global optimization libraries can be
relatively quickly modified to support portfolio management tasks, such as asset allocation and
dynamic portfolio optimization for hedging purposes. Portfolio optimization can be combined with
Monte Carlo simulations for multiperiod stochastic optimization applications, which are probably
cutting edge portfolio management techniques right now.

Some of the software for risk management was developed under a contract with Sailfish, Inc. but
we are entitled to use the generic technology.  Since we plan to port it to C++, it should further reduce
issues about ownership and intelectual rights.

Regarding data mining, parallel computing is indispensable for processing large data sets
contained in proprietary databases as well as wealth of data offered on the net. We do not
have integrated data mining applications yet, but we have sequential versions of generic
algorithms including statistical analysis tools, 
neural nets and global optimizers such as simulated annealing, Monte Carlo combined with Laplace
method and methods based on Langevin equation. A student is working on parallel implementation of
radial basis functions in the context of discovering option pricing formula in historical
market data, which could be redirected to data mining applications, since it is in very 
preliminary stages. We have done extensive benchmarks
of parallel Oracle and DB2 on SP-2 and other parallel systems. Furthermore, we are working
with an InfoMall partner to develop a proposal to the Financial Services Technology Consortium
for parallel data mining, where we would develop algorithms using their transparent parallel API
written in C++.


\section{Business Aspect}
\label{sec:bus}




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